Almost all about Rus-Hicks-Rhoades maps in quasi-metric spaces

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:7 Issue:2
Almost all about Rus-Hicks-Rhoades maps in quasi-metric spaces

Almost all about Rus-Hicks-Rhoades maps in quasi-metric spaces

Pages : 455-472

View : 70 | Download : 43

Publication Date : 2023-07-23

Article Type : Research Paper

Abstract :Let $insert ignore into journalissuearticles values(X, d);$ be a quasi-metric space. A Rus-Hicks-Rhoades insert ignore into journalissuearticles values(RHR); map $f : X \\to X$ is the one satisfying $dinsert ignore into journalissuearticles values(fx, f^2x); \\le \\alpha dinsert ignore into journalissuearticles values(x, fx);$ for every $x\\in X$, where $\\alpha \\in [0,1);$. In our previous work [37], we collected various fixed-point theorems closely related to RHR maps. In the present article, we collect almost all the things we know about RHR maps and their examples. Moreover, we derive new classes of generalized RHR maps and fixed point theorems on them. Consequently, many of the known results in metric fixed point theory are improved and reproved in an easy way.
Keywords : fixed point theorem, metric space, fixed point, stationary point, maximal element

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